Select all that apply.
A 0.200-kilogram ball sits on a shelf 2.00 meters from the floor and then falls to a point 1.00 meter from the floor. Ignoring any affects due to friction, at this position _____.
1) its mechanical energy is 3.92 J
2) its potential energy is 3.92 J
3) its kinetic energy is 3.92 J
4) its potential energy is 1.96 J
5) its kinetic energy is 1.96 J
6) its mechanical energy is 1.96 J
what are the formulas for this??
1,2,4
To solve this problem, we need to use the formulas for gravitational potential energy, kinetic energy, and mechanical energy.
The formula for gravitational potential energy (PE) is:
PE = m * g * h
where m is the mass of the object (in kilograms), g is the acceleration due to gravity (which is approximately 9.8 m/s^2 on Earth), and h is the height or vertical displacement (in meters).
The formula for kinetic energy (KE) is:
KE = (1/2) * m * v^2
where v is the velocity of the object.
The formula for mechanical energy (ME) is:
ME = PE + KE
where ME represents the total energy possessed by the object.
Now let's solve the problem.
Given:
- Mass (m) = 0.200 kg
- Initial height (h1) = 2.00 m
- Final height (h2) = 1.00 m
First, we can calculate the gravitational potential energy at the initial position:
PE1 = m * g * h1
Second, we can calculate the gravitational potential energy at the final position:
PE2 = m * g * h2
Next, since there is no mention of the object's velocity, we can assume it falls freely under gravity, which means all the potential energy is converted into kinetic energy.
Therefore, at the final position, the kinetic energy (KE) will be equal to the change in potential energy:
KE = PE1 - PE2
Finally, we can calculate the mechanical energy (ME) at the final position by adding the potential energy and kinetic energy together:
ME = PE2 + KE
By substituting the given values into the formulas, we can determine the correct answers from the provided options.